
Notice that if

, then

. Recall the definition of the derivative of a function

at a point

:

So the value of this limit is exactly the value of the derivative of

at

.
You have
Answer:
Step-by-step explanation:
Given are two functions represented one by graph and another by table
We can check the given statement one by one
1) 
Average rate of change = 
For g(x) avg rate of change
=
Hence g has a higher average rate of change than f.
True
2)f is linear and eventually exceeds g (f(0)>g(0) . True
3) True because y intercept is 10 for f while 8 for g
4) True because f(3) <g(3)
5) False both cannot be linear
In this problem, we need to plug in the given x values for

and find a and b.
When we plug in 1, we get:

Simplify:



We got our first statement about the values of the variables. If we find one more we can find those 2 variables.
We have another given root: 4.
Plug it in:




Now we have our second one. We can combine them:

I use elimination method which is easier here.
Multiply the top equation by -1:

Add them up:

Simplify:

Now we have a, we can plug in one of those equations to find b:



So, the answers are

and

.
Answer:
(1
, 2
)
Step-by-step explanation:
Given the 2 equations
7x - y = 7 → (1)
x + 2y = 6 → (2)
Multiplying (1) by 2 and adding to (2) will eliminate the y- term
14x - 2y = 14 → (3)
Add (2) and (3) term by term to eliminate y
15x = 20 ( divide both sides by 15 )
x =
=
= 1 
Substitute this value of x into either of the 2 equations and solve for y
Substituting in (2)
+ 2y = 6
2y = 6 -
=
( divide both sides by 2 )
y =
= 2 
Need the choices cant really answer your question